#### Filter Results:

#### Publication Year

1983

2016

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

We define the notion of ordinal computability by generalizing standard Turing computability on tapes of length ω to computations on tapes of arbitrary ordinal length. We show that a set of ordinals is ordinal computable from a finite set of ordinal parameters if and only if it is an element of Gödel's constructible universe L. This characterization can be… (More)

The Naproche project 1 (NAtural language PROof CHEcking) studies the semi-formal language of mathematics (SFLM) as used in journals and textbooks from the perspectives of linguistics, logic and mathematics. A central goal of Naproche is to develop and implement a controlled natural language (CNL) for mathematical texts which can be transformed automatically… (More)

- Peter Koepke
- 2012

We generalize standard Turing machines working in time ω on a tape of length ω to abstract machines with time α and tape length α, for α some limit ordinal. This model of computation determines an associated computability theory: α-computability theory. We compare the new theory to α-recursion theory, which was developed by G. Sacks and his school. For α an… (More)

Using the core model K we determine better lower bounds for the consistency strength of some combinatorial principles: I. Assume that A is a Jonsson cardinal which is 'accessible' in the sense that at least one of (l)-(4) holds: (1) A is a successor cardinal; (2) A = oE and 6 <A ; (3) A is singular of uncountable cofinality; (4) A is a regular but not… (More)

- D Kühlwein, M Cramer, P Koepke, B Schröder
- 2009

The Naproche project (Natural language Proof Checking) was initiated by Bernhard Schröder and Peter Koepke at the University of Bonn to focus on an interdisciplinary study of the semi-formal language of mathematics. A central goal of Naproche is to develop a controlled natural language (CNL) for mathematical texts and adapted proof checking software which… (More)

We generalize ordinary register machines on natural numbers to machines whose registers contain arbitrary ordinals. Ordinal register machines are able to compute a recursive bounded truth predicate on the ordinals. The class of sets of ordinals which can be read off the truth predicate satisfies a natural theory SO. SO is the theory of the sets of ordinals… (More)